Graph all asymptotes of the rational function.
F(x)=-x^2-5x+2/x+3
The rational function F(x)=-x^2-5x+2/x+3 has two types of asymptotes: vertical and horizontal.
To find the vertical asymptote, set the denominator of the function equal to zero and solve for x:
x + 3 = 0
x = -3
So, there is a vertical asymptote at x = -3.
To find the horizontal asymptote, compare the degrees of the numerator and denominator of the function. Since the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0.
Therefore, the graph of the rational function F(x)=-x^2-5x+2/x+3 will have a vertical asymptote at x = -3 and a horizontal asymptote at y = 0.